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Exhibit 32.1

UNIVERSAL COMPRESSION HOLDINGS, INC.
CERTIFICATION PURSUANT TO
18 U.S.C. SECTION 1350,
AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of Universal Compression Holdings, Inc. (the "Company") on Form 10-K for the period ending March 31, 2004 (the "Report"), I, Stephen A. Snider, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

(1)

The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and



(2)

The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/  STEPHEN A. SNIDER Stephen A. Snider
Chief Executive Officer
June 10, 2004

In connection with the Annual Report of Universal Compression Holdings, Inc. (the "Company") on Form 10-K for the period ending March 31, 2004 (the "Report"), I, J. Michael Anderson, Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

(1)

The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and



(2)

The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/  J. MICHAEL ANDERSON J. Michael Anderson
Chief Financial Officer
June 10, 2004

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Exhibit 32.1

UNIVERSAL COMPRESSION HOLDINGS, INC. CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002